## thechocoluver445 2 years ago If the direction angle of vector a is 100 degrees, with a magnitude of 8, and the direction angle of vector c is 60 degrees, with a mangitude of 13, find the magnitude of resultant a + c. I know how to set this up and solve it, but for some reason I can't get the right answer.

1. thechocoluver445

Here's what I did: |dw:1358034696496:dw| $x = \sqrt{8^2 + 13^2 - 2(8)(13)(\cos 140°)}$

2. zepdrix

Hmmm this is how I would do it :O So if we write our vectors in component form, we have,$\large \vec{a}=8\cos100 \hat i+8\sin100 \hat j$$\large \vec c=13\cos60 \hat i+13\sin60 \hat j$$\large \vec a +\vec c=\color{#3366CF}{(8\cos100+13\cos60)\color{black}{\hat i}+(8\sin100+13\sin60)\color{black}{\hat j}}$ Hmm since 100 degrees isn't a nice special angle, we're going to get ugly decimal values it seems... So punch that into the calculator, then to get the MAGNITUDE of that vector we'll do uhhhh the thing, yah... I'm a little confused where your formula for x is coming from. It looks similar to the law of cosines. Maybe I just haven't done these types of problems in too long c: heh

3. thechocoluver445

Yeah I used law of cosines. If I add up all of the things in your method, I don't get the correct answer.

4. zepdrix

ah ok c: lemme take another shot at it. sec.

5. zepdrix

Hmm I'm not quite sure :c In your attempt at the problem, where is the 140 degree angle coming from?

6. thechocoluver445

180 - 40 = 140.

7. thechocoluver445

(In the parallelogram)

8. mathmate

Did you have a positive or negative value for cosine?

9. mathmate

What did you get for the magnitude?

10. mathmate

@thechocoluver445

11. thechocoluver445

It would be negative since the 140 is to the left of the y axis

12. mathmate

Sounds good. So your magnitude is greater than 13? What did you get? Is it a matter of number of decimals?

13. mathmate

@thechocoluver445 are you still there?

14. thechocoluver445

It's supposed to be 9.8 but I keep getting 19. something!

15. thechocoluver445

I'm pretty sure my way makes sense, but I don't know.

16. thechocoluver445

I just realized that my way was correct. Since the resultant is opposite an obtuse angle, it must be the longest side of the triangle. Thus, 9.8 cannot be the right answer! So I was correct. Thanks to everyone for helping. :)

17. mathmate

19.8 is correct for the problem you have posted..

18. thechocoluver445

The answer key was just wrong, lmao!

19. thechocoluver445

Yeah, that's what I got lol!

20. thechocoluver445

She probably just forgot the 1 before the 9.8 haha

21. mathmate

The only thing you may want to check to see if there are typos. It is possible that they modified the question but forgot to modify the key (which is half of the current answer).

22. mathmate

So go with 19.8.

23. mathmate

Oh, so it's not a printed key! That make it even more probably that the answer is wrong.